Computational aspects of portfolio Credit Risk management

Philipp J. Schönbucher

Abstract: The implementation of portfolio credit risk models entails some specific numerical problems which are not often found in this combination in other contexts. Amongst these problems are the high dimensionality of the problem (easily hundreds or thousands of obligors), the presence of jumps and other low-probability events with large P&L impact and a pervasive scarcity of adequate data. In this talk we present a valuation method based upon the numerical inversion of the Laplace transform of the portfolio loss distribution and its application to the pricing of CDOs which requires a consistent evaluation of the portfolio loss distribution at several time horizons. This method is then compared to classical Monte-Carlo simulation techniques.